Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 16 - Cumulative Review - Page 568: 2

Answer

The number to the nearest three significant digits is $37.0\times {{10}^{-9}}$.

Work Step by Step

$\frac{\left( 612\times {{10}^{-6}} \right)\left( 15\times {{10}^{-9}} \right)\left( 2.7\times {{10}^{3}} \right)}{\left( 82\times {{10}^{9}} \right)\left( 8.16\times {{10}^{-12}} \right)}$, Combine the powers of $10$ by using the formula $\frac{{{a}^{x}}\cdot {{a}^{y}}}{{{a}^{z}}}={{a}^{x+y-z}}$. $\begin{align} & \frac{\left( 612\times {{10}^{-6}} \right)\left( 15\times {{10}^{-9}} \right)\left( 2.7\times {{10}^{3}} \right)}{\left( 82\times {{10}^{9}} \right)\left( 8.16\times {{10}^{-12}} \right)}=\frac{612\times 15\times 2.7\times {{10}^{-6-9+3}}}{82\times 8.16\times {{10}^{9-12}}} \\ & =\frac{612\times 15\times 2.7\times {{10}^{-12}}}{82\times 8.16\times {{10}^{-3}}} \\ & =\frac{612\times 15\times 2.7\times {{10}^{-12+3}}}{82\times 8.16} \end{align}$ Further simplify the above expression. $\begin{align} & \frac{\left( 612\times {{10}^{-6}} \right)\left( 15\times {{10}^{-9}} \right)\left( 2.7\times {{10}^{3}} \right)}{\left( 82\times {{10}^{9}} \right)\left( 8.16\times {{10}^{-12}} \right)}=\frac{612\times 15\times 2.7\times {{10}^{-12+3}}}{82\times 8.16} \\ & =37.04\times {{10}^{-9}} \end{align}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.